There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{({x}^{3} - 5)}{({x}^{3} + 5)})}^{9}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(x^{3} - 5)^{9}}{(x^{3} + 5)^{9}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(x^{3} - 5)^{9}}{(x^{3} + 5)^{9}}\right)}{dx}\\=&\frac{(9(x^{3} - 5)^{8}(3x^{2} + 0))}{(x^{3} + 5)^{9}} + (x^{3} - 5)^{9}(\frac{-9(3x^{2} + 0)}{(x^{3} + 5)^{10}})\\=&\frac{27(x^{3} - 5)^{8}x^{2}}{(x^{3} + 5)^{9}} - \frac{27(x^{3} - 5)^{9}x^{2}}{(x^{3} + 5)^{10}}\\ \end{split}\end{equation} \]

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